Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  scanf("%d", &n);
  int c = (int)sqrt((double)n);
  if (n == c * c + c)
    printf("YES\n");
  else {
    int d, e, flag = 1;
    n *= 2;
    for (int i = 1; i < c; i++) {
      d = n - i * i - i;
      e = (int)sqrt((double)d);
      if (d == e * e + e) {
        printf("YES\n");
        flag = 0;
        break;
      }
    }
    if (flag) printf("NO\n");
  }
  return 0;
}